Question

The sum of 5x?, -7x2,8x2, 11x2 and -9x2​

Answer 1

Answer:

and its nth term

= 2 + (n – 1 )3 = 2 + 3n – 3 = 3n – 1

and G.P is 1, x, x2, x3,… and its nth term is xn – 1 and sum of

arithmetic-geometric series be Sn and its term is (2n – 1)xn – 1 so

Sn = 2 + 5x + 8x2 + 11x3 +…+ (3n – 4)xn – 2 + (3n – 1)xn – 1 … (i)

xSn = 2x + 5x2 + 8x3 + … + (3n – 4)xn – + (3n- 1)xn … (ii)

Subtracting equation (ii) from (i), we get

(1 – x)Sn = 2 + [3x + 3x2 + 3x3 + … + 3xn – 1] + (3n – 1)xn